Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

Abstract

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach.

Keywords:

• piecewise-affine systems
• time delay systems
• Lyapunov–Krasovsky functional

Acknowledgements

The authors would like to acknowledge the financial support from Natural Sciences and Engineering Research Council (NSERC) and Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) for funding this research.